sensitivities

(L. Riegger, 2025)

Methods for linear and stochastic sensitivities analysis and uncertainty propagation, following the BIPM GUM (JCGM 102:2011).

Install

You can install the sensitivities module using pip:

pip install sensitivities

Usage

sensitivities.stochastic

The sensitivities.stochastic module provides functionality for stochastic sensitivity analysis. It allows you to stochastically sample input parameters from various, potentially correlated distributions and evaluate the sensitivities of a function to those inputs. Available distributions are

• Gaussian (given mean and standard deviation)
• Uniform (between lower and upper bound)
• Discrete (multiple discrete options)

Example for stochastic sampling:

from sensitivities.stochastic import sample, Gaussian, Uniform, Discrete
import matplotlib.pyplot as plt

def my_function(a, b, c=0, d=0):
    return a + b + c + d


samples = sample(
    my_function,
    [
        Gaussian(10, 0.05),
        Discrete([1, 2]),
    ],
    {"c": Uniform(-0.4, 0.4), "d": -100},
    corr=[("a", "c", 0.5)],
    n=100000,
)

plt.hist(np.array(samples), 100)
plt.show()

sensitivities.linear

This module contains the propagate_uncertainties function for propagation of uncertainties for a given function based on the principle of linear differentials. It makes use of the scipy function approx_fprime to calculate the partial derivatives of the given function.

Here is a simple usage example:

from sensitivities.linear import propagate_uncertainties

def my_function(x, y):
    return [x ** 2, x, y]

print(propagate_uncertainties(my_function, uncertainties=[0.1, 0.2], x0=[1, 1]))

This will output the propagated standard uncertainties and correlation matrix between the function outputs:

(
    np.array([0.2, 0.1, 0.2]),
    np.array([[1.0, 1.0, 0.0], [1.0, 1.0, 0.0], [0.0, 0.0, 1.0]])
)

Development

Setup development environment

uv sync --extra dev